A great many different techniques and apparatuses for making medical devices have been proposed over the years. In the case of balloons for angioplasty and other interventional treatments, production tends to be relatively labor intensive. Current balloon molds are typically fixed in size, and therefore specialized for molding a balloon of a particular configuration. In a typical setup, a tubular die is provided that has a center piece and two end caps. An elongate tubular body of starting material for the balloon to be formed is positioned in the center piece of the die, and the end caps for forming a cone and neck of the balloon are coupled to the center piece. The die is then typically positioned within a fixture, and pressurized air is supplied to the elongate tubular body to blow mold a balloon therein. Heat applied to the exterior of the die softens material of the elongate body to facilitate its plastic deformation during blow molding. Once formed, the balloon can be removed from the die for further processing. While this general technique and apparatus has worked well for many years, it is not without drawbacks, notably the requirement to use a dedicated die for each balloon configuration to be molded.